Question

What is the correct expression of position vector rcb (in feet)?

Answer 1

4i+j-2k

Explanation:

The missing figure in this problem as been attached, as we can see the figure is a 3-D figure consisting of rods with point C and B.

Using the figure we can find the value of position vector
`r_(cb)`

r
`_(CB)`=
`r_(b)`-
`r_(c)`

As we know , a position vector is the difference of position vector of ending point to the position vector of starting point, here the starting point is C and ending point is B. Hence, the expression above.

We need to first find
`r_(b)` and
`r_(c)`

Using the figure:

`r_(b)` =0i+4j+2k

`r_(c)` = -4i+3j+4k

r
`_(CB)`=
`r_(b)`-
`r_(c)`=(0i+4j+2k) - (-4i+3j+4k)

r
`_(CB)`=4i+j-2k (feet)

Magnitude of
`r_(cb)`=
`\sqrt{4^(2)+(1)^(2)-2^(2) }`=
`√(21)`=4.583 ft